Let R be the region bounded by the curves y = 1 x2 and y =

Question:

Let R be the region bounded by the curves y = 1 – x2 and y = x6 – x + 1. Estimate the following quantities.
(a) The -coordinates of the points of intersection of the curves
(b) The area of R
(c) The volume generated when R is rotated about the x-axis
(d) The volume generated when R is rotated about the y-axis